Question

Find the area enclosed by each of the following figures

Answer 1

i) the area of triangle is 1/2 * 4* 2=4 sq units

and area of square is 4*4= 16 sq units

16+4=20 sq units

ii) area of trapezium = a+b/2 *h

= 18+7/2 * 8

=100 sq units

area of square = 18*18= 324 units

= 324+100=424 sq units

iii) similarly using the formula a+b/2*h

area of figure is= 384 sq units

ii)

Answer 2

Given,

Three figures are a mixture of the main squares, rectangles, triangles, and trapeziums.

To Find,

The area is enclosed by the figures.

Solution,

(i)For the first figure, it is a figure consisting of a triangle and a square of 4 cm each side.

The area of the triangle is $\frac{1}{2}$× 4× 2=4 $cm^{2}$.

The area of square with a length of 4 cm each side, is 4×4= 16 $cm^{2}$.

So the total area of the figure is 16+4=20 $cm^{2}$.

ii)For the second figure, it is a figure consisting of a trapizium with height of 8 cm,parallel sides of 7cm,18cm and a square of 18 cm each side.

Atfirst the area of square is 18×18= 324 $cm^{2}$.

area of trapezium = $\frac{a+b}{2}$×h.

= $\frac{18+7}{2}$ × 8.$cm^{2}$

=100 $cm^{2}$.

So the total area is

= 324+100=424 $cm^{2}$.

iii) For the third figure, it is a figure consisting of a trapizium with height of (28-8)cm=8 cm,parallel sides of 6cm,15cm and a rectangle of 20 cm and 15 each side.

Area of rectangle=(Height×Breadth)=(20×15)=300$cm^{2}$.

Similarly using the formula ,

Area of trapizium is= $\frac{15+6}{2}$×8 $cm^{2}$=84$cm^{2}$.

Total area of the figure = Area of rectangle+Area of trapizium=300+84=384$cm^{2}$.

Hence, The area of figure (i) is 20$cm^{2}$ .(ii) is 424$cm^{2}$ .(iii) is 384$cm^{2}$ .